The Kreuzaxt is, in mutch of the German speaking world anyway, an outdated tool. It was used centuries ago for the job of cleaning out mortises and also for dressing joints much like Americans would have used a slick.

The Kreuzaxt was replaced a very longtime ago by a development of it. Some time along the line, they removed the wooden handle (but left the socket) and also the mortising chisel was removed. We are left with a tool known as Stossaxt or Stichaxt, which is today a very very common tool.

This tool is used on timbers just above knee high for applications where a slick might be used in other traditions. It is single beveled, and you use it by leaning into the tool and letting the mass of your body do the work. It is not a primary joint cutting tool, but a fine finishing tool (and a very good one at that)